Tax dodgers will get an earful this week in Brussels. With public outrage soaring over the perceived failure to pay their dues by the likes of Amazon, Eric Schmidt's Google and other squillion-dollar transnationals, European leaders will feel bound to berate and deplore, bemoan and declare. And that will pretty much be that.

An EU summit on Wednesday in Brussels will declare combatting tax evasion and VAT fraud to be the next big common European endeavour. David Cameron will claim credit for the offensive and seek to salvage his dwindling authority – at home and in Europe – by promising to put tax dodgers at the top of the G20 agenda.

There is certain to be enough hot air to propel the 30 leaders ballooning over Brussels. But a draft of what the summit will decide, obtained by the Guardian, shows that they will decide very little. The eight-page document drafted on Friday speaks of "reflecting" on this, "accelerating" that, "responding" to this. And returning in December to have another try at policy-making which has been stuck for years because of resistance from banking secrecy havens such as Austria and Luxembourg.

The real game-changing moves in the effort to clamp down on corporate tax dodging are coming from the Obama administration. "The US pressure is immense," said an EU diplomat. "It's a real steamroller going on at a global level."

The Europeans are playing catch-up. But they won't catch up this week. Instead, the real heavy lifting, leading to another, more important summit next month, is an almighty tussle over how to emerge from four years of financial and currency crisis. More the political than the financial fallout. How, when, and in what form should economic and fiscal policy-making be pooled in the eurozone in order to put political flesh on the very brittle bones of the currency union, a fragility cruelly exposed by the turmoil of the past three years?

This is crystallising into a straightforward Gallic-Teutonic contest, with a weak President François Hollande in Paris issuing challenges to a strong Chancellor Angela Merkel in Berlin who blithely ignores the French entreaties.

A detailed survey of eight EU countries last week from Pew, the US pollsters, underlined the yawning gap between France and Germany and Berlin's isolation on the euro crisis. Number-crunching the sophisticated data, the pollsters concluded that the Germans were living on a different continent from the rest of the EU, such were the divergent views.

Guido Westerwelle, the German foreign minister, is alarmed at the implications of this for Germany's image and place in Europe and the world. But Merkel seems quite unfazed, happy to be the whipping girl for everyone else's frustrations provided the policies work – the aim being to get Europe fit, competitive and efficient for the global contest that could leave it lagging at the back.

As long as the eurozone's hospital ward keeps taking the medicine and the pills are working, the patients can whinge all they like about the German doctor. This is the impression that Merkel gives.

Hollande, in what appeared an attempt to show that he is not asleep at the wheel, last Thursday set out his vision for the eurozone, for the first time in any detail. Predictably, it clashed utterly with Berlin's. It was very French, almost identical to proposals previously tabled by his predecessor, Nicolas Sarkozy, and previously rejected by Merkel. Hollande said he wanted a eurozone government within two years, with its own budget, tax base, and eventually pooled debt issuance or eurobonds. The idea is that Hollande and other national eurozone leaders would meet once a month to decide policy, supported by a new eurozone secretariat.

But after three years of crisis management, it is absolutely clear that the Germans will not accept liability for anything they do not control. That means eurobonds or German taxpayers' money being used to finance other governments automatically will not happen for a very long time. Nor will the Germans countenance a common eurozone fund that would be used to prop up other countries' stricken banks.

"It's a good relationship, but very difficult," said Peter Altmaier, the German environment minister. "There are things that the French don't understand about Germany and that Germans don't understand about France."

In public, the Germans are wary of lecturing the French about how to put their own house in order. The Dutch are less shy. The prime minister, Mark Rutte, responded to Hollande's blueprint by telling him to forget about Europe and to tackle France.

As France wrestles with recession, soaring unemployment, missed debt and budget targets, and structural stagnation, Merkel also is keen to see Hollande get to grips with a domestic agenda.

The European commission has agreed to give Hollande an extra two years to meet the euro rules on the budget deficit target of 3% of GDP. But Berlin is leaning strongly on the commission to force structural economic reforms on France in return for the concession. "France is the really big concern," said Norbert Barthle, of Merkel's Christian Democrats. "We're prepared to give them two years but right now [commissioner] Olli Rehn has to connect this to strict conditions. Binding. Otherwise the German government will not support it."

There is a long history of Franco-German friction at the heart of the EU. But things have rarely been so imbalanced as they are now. As the summits come and go, it will be September at the earliest, when Merkel hopes to win a third term, before serious accommodation can begin to be reached on both sides of the Rhine.

"Hollande's and Merkel's ideas on European economics are so far apart," said Munich's Süddeutsche Zeitung on Saturday. "The economic dynamics are working in Merkel's favour. So Merkel is playing a waiting game. If she's re-elected, he will have to move."

Five things to watch out for

• Monday sees the first in a series of votes on the same sex marriage bill, with rebellious Tory MPs threatening to derail its passage with an amendment to extend civil partnerships to heterosexual couples.

• Major Tim Peake will be announced on Monday as the UK's first 'official' astronaut in 20 years. He will join the crew on the International Space Station in 2015.

• On Wednesday the IMF will be in London to deliver its annual verdict on the health of the UK economy.

• The Hay Festival of arts and literature begins on Thursday in Powys.

• In the first all-German Champions League final, Bayern Munich face Borussia Dortmund at Wembley stadium on Saturday night.

• This article was amended on 24 May 2013. The original suggested that the Hay festival was in Herefordshire; Hay-on-Wye, the location of the festival, is just over the Welsh border in Powys.